Introduction

The pattern of medical practice varies with specialties and the activity level varies with individuals. The F.T.E is an attempt to standardize practice size to a common denominator. The F.T.E results in a single value, for each physician, which quantifies his/her practice relative to what is considered a full load. A physician with an activity level above the "normal" will have a FTE value greater than one. A physician with a practice size below the "normal" will have a FTE value of less than one.

The F.T.Es, regardless of the methodology implemented, should be able to accomplish at least three objectives.


• Provide a consistent method for the quantification of the Aggregate Supply.
  
• Provide a consistent basis for intra-interprovincial evaluation of physician supply.
  
• Provide a consistent basis for the analysis of physician supply throughout the years.

The actual value of the FTE is methodologically sensitive. There is no "best" measure and therefore, all measures of full time equivalence are to some degree arbitrary. We adopted the FTE methodology developed by National Health and Welfare. The National Methodology uses physicians payments as a proxy to evaluate activity levels (workload). To account for differences in patterns of practice and fee schedules, the FTE calculation is specialty specific.

Full time is defined as those earning between the 40th and the 60th percentile. Typically, the payment distribution is skewed because there are a large number of physicians working (earning) just part of the year. The benchmark calculation is based on all physicians reporting at least one claim in each of the 4 quarters. The exclusion of the "part year" physicians in the bench mark calculation underscores how sensitive the benchmark and, ultimately, the supply count, is relative to the underlying distribution. If the "part year" physicians were included, the benchmarks would have been lower and the resulting supply count higher.

Every physician's payment is compared to the benchmarks and the FTE is calculated according to one of three possible situations:


• The payment is lower than the 40th percentile. the FTE = payment/p40 . the FTE ranges from 0 to 1 (exclusive).
  
• The payment falls in between the 40th and 60th percentile (inclusive) the FTE = 1 and it defines "the typical" full time physician.
  
• The payment is higher than the upper benchmark (60th percentile) the FTE = 1+ natural log (payments/p60) . The logarithmic relation prevents high income physicians from having very large FTE. A physician earning 4 times the 60th percentile will have a FTE=2.4 instead of 4.

Full Time Equivalent Algorithm in Detail

The relationship between payments (earnings) and FTE values is not a linear one, and therefore, the investigator should be fully aware of the implications. In situations, such as workload, where the FTE counts is used in the denominator, the analyst should either decide to use the "typical" workload of a "typical" physician (FTE=1) or to ensure that he/she understands how the distribution (small , typical and large practices in this case) may affect the results:

Example:



Let us have three regions with the same output.

Area A is served exclusively by a large number of physicians with small practices (typical of remote regions).

Area B is served exclusively by "typical" full time physicians (FTE=1).

Area C is served by one physician with a very large practice.

Let us also assume that the lower benchmark=40 and the upper=60.

For illustrative purposes, there is a one to one relationship between payments and output.

Table 1: FTE Calculations with Variability


Area	A	Area	B	Area	C
output	FTE	output	FTE	output	FTE
30	0.75 (30/40)	40	1.0	100	1.51 (1+ln(100/600))
35	0.875 (35/40)	60	1.0	-	-
35	0.875 (35/40)	-	-	-	-
100	2.50	100	2.0	100	1.51

While the three areas have the same output of 100, the workloads (output/total FTE) are 40, 50 and 66 respectively.

Should the areas not have had a "bias" distribution, that is, a relatively similar proportion of physicians by practice size, the workload would have been similar.

The full potential of the national F.T.E (or any other for that matter) cannot be realized if the investigator does not fully understand the premises behind the algorithm:

Homogeneity

Are we sure that the practices' profile and fee structure are similar for the groups under consideration? Only the yes answer will validate using payments as a proxy for workload.

Distribution

A perfect normal distribution is the ideal situation. Badly skewed distributions are the norm. The distribution underlying the national algorithm is skewed towards lower values. (recall the 4 quarters rule in the benchmark calculation).

A Bimodal distribution, two groups gravitating around two central values, is a good indication of poor homogeneity. That was the case with Internists and Pediatricians. In fact, in the case of pediatricians, there were two distinct groups: a) the GFTs, working for the University and b) the generalists working in the community. The payments captured for the former group was extremely low as their earnings are mostly salaried/teaching. A mechanical application of the algorithm produces nonsensical results.

Benchmark Stability

The larger the number of observations the more stable the benchmarks. This has to do with the "positional" nature of the benchmarks. Unlike the mean or the standard deviation, which describes certain attributes of the distribution as a whole, the nth percentile is simply the value below which n/100% of the observations are found. Benchmark stability has to do with the difference between ordered values, or the magnitude of the change if the benchmark were defined to be the value at the nth+1 percentile instead of the nth.

Table 2: Difference Between Ordered Values


position	nth-3	nth-2	nth-1	nth	nth+1	nth+2	nth+3
value group 1	10	10.2	10.4	10.5	10.5	10.6	10.7
value group 2	10	15	25	40	50	55	60


The benchmark defined by nth percentile is much more stable for group1. It makes little difference whether the benchmark happened to be defined by the nth, nth+1...nth+n, or by nth, nth-1...nth-n percentile. In turn, the magnitude of the difference between nth and nth+1 observation is influenced by the number of physicians in the distribution. The larger the number of observations, the more stable the percentiles, the benchmarks, and hence the more consistent the FTE counts. In fact, for the year 1994, the number of GP claiming in each of the quarters was 821, and the average percentage change from the Nth to Nth+1 position was .009%. In contrast, for specialists the number of mds ranged from 71 to 199, depending upon the specialty, the average percentage change was from 6 to 10%.

Consistency and Changes Over Time

While the issues of homogeneity, nature of the distribution and benchmark stability will define the "true" picture, a good understanding of changes over time will ensure a consistent count of physician supply throughout the years.

In Manitoba, since 1991, there has been a steady decline in Physician's earnings, that is, the income that we are able to capture from the database. (for many reasons). Does the decline on payments, the variable at the algorithm's core, change the FTE calculation...? The short answer is a qualified no, this is because the income decline happened to be across the board, random, and it introduced no bias.

The following example illustrates a situation where income in year 2 increased across the board, twice as much relative to year 1.

Table 3: FTE Calculations


year	p10	p20	p30	p40	p50	p60	p70	p80	p90	p100	total
1$ FTE	1 0.25	2 0.50	3 0.75	4 1	5 1	6 1	7 1.15	8 1.29	9 1.41	10 1.51	55 income 9.86 f.t.e.
2$ FTE	2 0.25	4 0.50	6 0.75	8 1	10 1	12 1	14 1.15	16 1.29	18 1.41	20 1.51	110 income 9.86 f.t.e.

Obviously, the income increase does not alter any of the elements underlying the distribution, that is, the number of observations, and the relative evaluation of an individual relative to everybody else. Notice that the increase (decrease) of income would have a different meaning if it were due to increases (decreases) on prices or quantity alone. In the former case (prices), the same number of physicians would be operating at a constant workload but at different price levels. There would be no changes in FTE nor in workload. In the latter case (quantity) the same number of physicians would operate at a constant price but at different workload levels. No changes in FTE but the workload would be twice as much as the first year.

For completeness sake, let us examine the case where everybody gets a constant increase (decrease) in income. In the following example, income in year 2 increases by a constant of, let us say, $2.

Table 4: FTE Calculations Constant Increase


year	p10	p20	p30	p40	p50	p60	p70	p80	p90	p100	total
1$ FTE	1 0.25	2 0.50	3 0.75	4 1	5 1	6 1	7 1.15	8 1.29	9 1.41	10 1.51	55 income 9.86 f.t.e.
2$ FTE	3 0.50	4 0.66	5 0.83	6 1	17 1	8 1	9 1.11	10 1.22	11 1.31	12 1.40	75 income 10.03 f.t.e.


The increase from 9.86 to 10.03 FTE cannot be validated. If we assume that the $2 increase in income is due to prices alone, then in year #2, we would expect the same number of physicians working at the same workload level of year #1.

The discussion above shows the need for a comprehensive understanding of the factors determining the FTE final count, as well as the need for testing for significant changes in the distribution before changes of FTE over time can be validated.

Formalizing the FTE Function

Changes in the F.T.E counts is the result of changes in the underlying distribution. The distribution is a function of the number of observations (heads) and income. Income, in turn, is a function of prices (fees) and quantity (claims). Overall,

Changes FTE=f(x) changes (heads, income (prices, quantity))

Changes in heads (number of observations) affects the final FTE counts in following ways:



• Increases (decreases) of heads in year 2 relative to year 1 changes the benchmark.
  
• In a distribution of an even numbers of heads the lower and upper benchmark are exactly the income of those physician at the 40th and 60th percentile.
  
• If we increase the numbers of heads, let us say, by one, then the new benchmark will be some average of:

  new benchmark = ((income at p40) + (income at p40+1))/2

So far we can establish the following relationship: increases (decreases in heads, changes the benchmark and hence the final FTE count. The direction of the change will depend on "the bias" introduced by the increase or decrease of heads.

Let us think of the distribution in terms of three segments:
1. The lower income comprised by the 40% of the observations.
   
2. The middle income comprised by 20% of the observations
   
3. The upper income comprised by 40% of the observations.

Suppose the distribution in year 2 were to contain the income of three new physicians, everything else being constant, the impact of these three physicians on the benchmark would be as follows:


• If the three physicians were in the lower income group, then the benchmarks would be LOWER and hence the final count HIGHER.
  
• If the three physicians were in the higher income group, then the benchmarks would be HIGHER and hence then final count LOWER.
  
• If one of the three physicians were each in one of the three income groups, then the benchmark would be very similar to the year 1, and hence whatever difference of FTE in year 2 would be due to the legitimate contribution of the three new practitioners.

Having in mind the latest, "unbiased" example, we can formulate the following relationship: "In absence of a bias distribution, everything else being equal, there is a direct relationship between Heads and FTE counts... the greater (the lower) the number of heads the greater (the lower) the FTE count".

Changes in FTE as a Function of Changes in Income

Prices (fees) are largely fixed and given. A physician wanting to increase income will do so by increasing quantity. (Strictly speaking a physician has limited opportunity to maximize income by changing the profile make-up, that is, shifting towards higher fees tariff). It follows that when holding Heads constant, changes in FTE are largely due to changes in quantity.

Testing and Validation of FTE Count Over Time

We already stated that income has steadily declined over the 4 fiscal years for which we have data. We have hypothesized that as long as Income changes are equally felt across the board, the distribution and the FTE counts should be comparable from year to year, and finally, changes in FTE counts are due to a complex relationship between changes in heads, quantity, and the role of heads in the benchmark determination.

The testing and validation process will be approached as follows:

In the first stage we will keep Heads constant. We will work with those physicians who have well established practices: that is, those active throughout the 4 years. By keeping heads constant we will achieve a twofold simplification...


• Changes in FTE as a function of quantity only.
  
• As discussed in the previous section (Formalizing the FTE function) changes in heads no longer play a role in the benchmark determination.

Equally important, this subgroup of physicians, which accounts for 68-70% of the total heads and for about 85% of the total income, are the group least susceptible to respond to short run policy changes and therefore the most stable and predictable. This latter characteristic - stability and predictability - allows us to approach the testing intuitively as well as statistically. In the second stage, we will include everybody, that is, we will let heads fluctuate and the testing will be purely about the significance of changes in the distribution over time.

The income and FTE for the 742 gps working throughout the period 1991 to 1994 inclusive is as follows:

Table 5: Income and FTE Calculations


fiscal year	income (millions)	FTE (n=742)
91/92	90.26	684.50
92/93	91.06	680.95
93/94	88.25	685.52
94/95	83.08	675.35

If the income fluctuation is the same across the board, then we should expect the benchmark to behave similarly.

Table 6: Benchmark


fiscal year	income (millions)	lower benchmark (thousand)	upper benchmark (thousand)
91/92	90.26	97.5	138.0
92/93	91.06	100.2 +3	141.0 +3
93/94	88.25	95.6 -5	136.0 -5
94/95	83.08	87.6 -8	130.0 -6


As expected, the benchmarks moved in the same direction as income, and except for the lower benchmark for the year 94/95, the magnitude of the change for the lower and upper benchmark is about the same.

If we think in terms of three income groups - the lower income with 40% of the observations (heads), the middle income with 20% of the observations, and the upper income with 40% of the observations - then the extreme decrease in the lower benchmark for the year 94/95 suggests a rather drastic change in the low income distribution.

It has been repeatedly argued that a meaningful understanding of changes of FTE over time hinges on an equally good understanding of changes in the underlying distribution. After all, the very reason for the F.T.E algorithm arose from the need to deal with skewness in the income distribution (in a perfect "normal" income distribution the sum of the ratio income over mean income is exactly the same as the number of heads). A simple glance at how this distribution shifts around a "normal" value yields a wealth of information about the direction and magnitude of the impact of policy changes in the three income groups, and, ultimately, a detailed account of the increases/decreases of FTE counts from year to year. Such a "normal" value would be the ratio - sum of FTE: heads - that we should expect if the distribution was perfect; that is, if the income increase between the (nth+1)-nth physician were a constant.

Example: Lower income

It was already suggested that the decrease from 685 to 675 FTE in 1994 relative to 1993, was largely due to changes in the low income distribution. Given the fact that the lower income part of the algorithm is a linear relation (sum of FTE=sum of (income/lower benchmark)), in a "perfect" income distribution, we should expect the average FTE to be =0.50.

The following table shows the behaviour of the low income group.

Table 7: FTE Low Income


year	heads	FTE	average FTE over heads	average months active per year
91	296	144	0.487	9.69
92	296	144	0.506	10.48
93	296	151	0.511	10.64
94	296	138	0.465	9.74

Clearly, the decrease in 1994, from 151 to 138 FTE, is due to a drastic shift of the distribution towards lower income (quantity) values ... Similarly, the increase in 1992 from 144 to 150 FTE is due to a shift towards higher income (quantity) values. In the latter case, the increase (1992) represents the "full year" work of those who started their practice in 1991. In the former case, the decrease represents the "part year" work of those who close their practice down in 1994. Whether they were a newcomer in 1991, or whether they departed in 1994, the lower FTE reflects their "part year" practices. Still, the extreme low average FTE value for 1994 suggests an overall decrease in quantity. If we break up the 1994 FTE of those who departed and those who stayed, we would be able to fully account and explain the changes of 1994 relative to 1993.

Table 8: Departing and Full Year FTE


year	heads	FTE	average FTE over heads	average months active
93	296	151	0.511	10.64
departing 94	31	9	0.286	5.25
full year 94	265	129	0.486	10.24


The decrease of 13 (151-138) FTE in 1994, is due to 9 FTE who retired sometime in 1994. We can predict that an extra 4 FTE departed as well but have not formalized status with Manitoba Health (i.e.: number still active). The decrease in the average number of months active reinforces the argument for the relationship FTE-quantity.

We have proved for the lower income segment of the algorithm the following:


• The income fluctuations do not alter the algorithm's consistency and hence comparisons over time are sound.
  
• When heads are held constant, changes in FTE are function of changes in income (quantity).

Example: Upper Income (non linear relationship)

The logarithmic nature of the function makes comparison over time misleading and difficult to interpret. By definition, the marginal increase of log(y) is decremental.

Table 9: Upper Income Non-Linear Relationship


Y	% change	FTE 1+ln(y)	% change ln(y)
2	-	1+ 0.69	-
3	1.5	1+ 1.09	1.23
5	1.6	1+ 1.61	1.25
9	1.8	1+ 1.20	1.22
11	1.2	1+ 2.34	1.04
30		12.93

The practical implication is that, keeping quantity (Y) constant, the sum of ln(Y) (FTE) will depend of the "shape" of the distribution.

If we re-arrange the above distribution into one which less skewed...

Table 10: Less Skewed Distribution


Y	FTE 1+ln(y)
4	1+1.39
5	1+1.61
5	1+1.61
8	1+2.08
8	1+2.08
30	13.77


The increase from 12.93 to 13.77 FTE is a non-sensical result since, as shown, changes of FTE is a f(x) of income (quantity) and, in this case income (Y) is constant.

Changes in FTE

The following table illustrates changes in FTE from 1993 to 1994.

Table 11: Changes in FTE


year	heads	FTE	number of claims	highest income
93	296	384	3086	789673
94	296	388	3085	636065


The increase of 4 FTE cannot be validated. The number of claims (mostly ambulatory visits) for all practical purposes is the same. Notice, however, the huge decrease in the most extreme income value. Clearly, the distribution in 1994 shifted away from extreme values and the increase in FTE is just a "numerical" reflection of the logarithmic nature of the algorithm.

FTE and the Manitoba Experience

In 1991 National Health & Welfare calculated F.T.Es for 17 specialties across the country. In Manitoba, except for General Practitioners, the relatively small numbers of physicians within these specialties forced us to collapse them into "parent" groups.

For the fiscal year 94-95 the following are the counts for heads (numbers of individuals) and FTE.

Table 12


parent group	specialties	heads	FTE
General Practitioners	Urban Gps Rural Gps Emergency * -	706 349 7 1062	498.535 305.577 4.303 808.415
Psychiatry	-	133	111.049
Pediatrics	specialists generalists ** -	38 68 106	38.000 55.689 93.689
Obstetrics	-	63	58.145
Medical	internal specialists generalists ** neurology geriatrics * rheumatology dermatology -	159 24 21 3 8 13 228	127.568 16.219 16.576 0.556 5.294 14.532 180.745
General Surgery	-	81	67.454
Surgery	thoracic plastic urology orthopedic neurology EENT (eyes) EENT (otorhino) EENT * (out prov) -	10 12 17 32 5 35 23 4 138	10.23 12.21 17.05 28.57 3.68 33.19 14.34 0.02 119.28
Grand Total	-	1811	1438.78

* mostly salaried (ie: we do not capture activity very well)

** Internist and pediatrics generalist/specialists... see discussion on (f).


The small numbers of observations (for physicians other than GPs) presented us with no small challenges. As already discussed, small numbers make the distribution unstable. The process of aggregation into "parent" groups raised the issue of homogeneity. On the plus side, the fact that specialist practices tend to be well established - that is, not very extreme values and distribution not too skewed - makes the number of heads a good anchor to relate to. Furthermore, we had the assistance and the approval of external sources, such as the Dean's office and the Manitoba Medical Association.

From a methodological point of view, we devised several validation approaches, chiefly among them "distribution super-imposing": that is, comparing the sub-specialty distribution against the parent distribution, in search and/or correction of imbalances, as discussed in the section titled " Formalizing the FTE function ".

Generalist / Specialists

Pediatrics and Internists were broken into two distinctive groups: Generalists and Specialists.

The Specialists component are comprised by physicians working for the University. These specialists, Geographic Full Time (GFT), are mostly salaried and hence we capture a small portion of their practice in the form of fee-for-service payments. Out of the 106 registered pediatricians, 38 were identified as specialists with a FTE value of 1. The remaining 68 individuals were identified as generalists with an aggregate FTE value of 55.7.

In the case of Internal medicine, within the Medical parent group, 24 physicians were identified as Generalist and 159 as specialists. In the former case, FTE were calculated based on 24 observations (FTE=16.2) and in the latter case, the FTE (127.6) were based on the Medical Parent group (cardiologists, neurology, geriatrics, rheuma and dermatology).

The identification process was carried out using two parallel approaches:


• compilation of external sources.
  
• identifying specific clinic's profiles for the groups under consideration.

The external sources consisted of several lists drawn by the Dean's office and Dr. Coke's for the internists and Dr. Postl for the pediatrics. The disadvantage of such an approach is that the lists are time specific, in this particular case, it reflected the situation as of 1995. The profile approach (see ancillary data sets appendix) when compared against the lists, proved to be a good, yet not perfect, discriminatory tool. Consequently, the formats (cd 'bogdan/fmtlib/gralist') and the FTE (ftedeliv cd '/dsd1/bogdan/ftedel94') can be used for years not too far apart from 1994-1995.

The following are the specific algorithms:

1). Generalist

Internist Generalists:

first criteria----> mdcbloc '01' internal medicine. drcoke definition the most reliable of all external sources. (short list and no human error) Wpg specialist list and G.F.Ts lists least reliable: hundreds of numbers and several levels of errors. (names->numbers->fake numbers->typing.)

Most freq tariff----> office visits likely generalists. consults and specifics tariffs (ie:electros,lung function,etc) likely specialists.

Defining generalists:

first level---->if mdcbloc='01' & drcoke= no label or General and most freq tariff=office visits.

second level----> From D.r Coke list I know, for example, that Gastro has Office visits as the most frequent tariff... From the first level generalist definition I look for gastro in the gft or wpg or also certified list... if found I reclassify this physician from generalist to specialist. note: "Interested in" does not qualify for specialist.

2) Pediatrics

Defining generalist:

first stage--> from the G.F.T list those without specialty (blank) or community, ambulatory or emergency are generalists.

second stage----> from "also certified" those with OTHER than blank or community are converted to specialists.

third stage---> those with most freq tariff OTHER than Office visits are converted to specialists.

fourth stage----> those with consult gt than 0 and ratio consult/amb ge 30% are converted to specialists. note: "also interested in" does not qualify

fifth stage----> phynos 1052, 1688, 2348, 2936 converted to specialists (dr brian postl' list)

Proportional Allocation and Aggregate Measures of FTE

As discussed in Appendix 1, "geographic aspects in physician supply", we developed a dynamic scheme by which we can track practice location. The physician location allows us to allocate FTE proportionally to the number of visits provided while practicing in different communities. For example, a physician may be assigned to area A and B, each for six months at the time. However, if 2/3 of the total visits were provided while in area A, then 2/3 of the FTE is allocated to area A and 1/3 to Area B. This method accounts for the substantial mobility of many rural physicians, while still allocating FTE contributions according to activity levels.

(For a detail description of the algorithm linking the physician location to the claims file, see appendix 1, "Geographic aspects in the physician supply").

Since for every patient-physician contact, we know the residence of the patient and the physician place of practice, we can express Aggregate FTE, that is, the number of resources used/available in terms of:

• Supply : IN AREA SUPPLY (I.A.S) The total numbers of FTE available per geographic area.
  
• Utilization: Area Resident Utilization. The total numbers of FTE (resources) used up by residents of a geographic area, regardless where the contact occurred.
  
• Supply/utilization: (within supply/utilization) The total numbers of FTE (resources) used up by residents, using physicians available locally.